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Analytical derivation of the Hückel “4n + 2 rule”

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Abstract

The “4n + 2 rule” is derived analytically at the level of the simple Hückel theory for neutral even-membered chains, their double ions, as well as cations and anions of the odd-membered chains, by determining the first order energetic effect of the ring closure. The topological background of the “4n + 2 rule” is also briefly discussed.

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Notes

  1. The author is grateful to a Referee for calling his attention to Refs. [4, 5].

  2. The author is indebted to a Referee for calling his attention to Ref. [7].

  3. In Ref. [5] the even more compact, but of course equivalent, form \( D_{1(2k)}={\frac{(-1)^{(k-1)}}{2k+1}}\left(1+\sec{\frac{\pi}{2k+1}}\right) \) was given (in our notations). In Eq. 3 we kept the formula as it was obtained by us.

  4. In the positive ion we omit some terms as compared with the neutral molecule, for the negative ion we add the same term once more but with opposite sign, as the two ends necessarily belong to different subsets (starred and not starred) of carbons.

References

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  3. Schleyer PVR (2008) Girona seminar on aromaticity. Girona, Spain

  4. Karadakov P, Castaño O, Fratev F, Enchev V (1981) Chem Phys Lett 78:560

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  8. Landau LD, Lifshitz EM (1974) Kvantovaya mekhanika, 3rd edn. Nauka, Moscow

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Acknowledgments

Supported in part by the Hungarian Scientific Research Fund (grant OTKA 71816).

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Authors and Affiliations

  1. Chemical Research Center, Hungarian Academy of Sciences, P.O. Box 17, 1525, Budapest, Hungary

    István Mayer

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  1. István Mayer
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Correspondence to István Mayer.

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Dedicated to Dr. Sándor Suhai on the occasion of his 65th birthday and of our nearly 40 years of acquaintance.

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Mayer, I. Analytical derivation of the Hückel “4n + 2 rule”. Theor Chem Acc 125, 203–206 (2010). https://doi.org/10.1007/s00214-008-0504-x

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  • DOI: https://doi.org/10.1007/s00214-008-0504-x

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